Problem: Rewrite as a simplified fraction. ${3.\overline{89} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 389.8989...\\ 1x &= 3.8989...\end{align*}}$ Subtracting the two equations, we have: ${99x = 386}$ ${x = \dfrac{386}{99}} \text{or} {3 \dfrac{89}{99}}$